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Popular >

simplify log_{e}(4x^2y^5)

Solution

simplify

lo g_{e} (4 x^{2} y^{5})

Solution

2 ln (2) + 2 ln (x) + 5 ln (y)

Solution steps

lo g_{e} (4 x^{2} y^{5})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{e} (4 x^{2} y^{5}) = lo g_{e} (4) + lo g_{e} (x^{2}) + lo g_{e} (y^{5})

= lo g_{e} (4) + lo g_{e} (x^{2}) + lo g_{e} (y^{5})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{e} (x^{2}) = 2 lo g_{e} (x)

= lo g_{e} (4) + 2 lo g_{e} (x) + lo g_{e} (y^{5})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{e} (y^{5}) = 5 lo g_{e} (y)

= lo g_{e} (4) + 2 lo g_{e} (x) + 5 lo g_{e} (y)

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (4) + 2 lo g_{e} (x) + 5 lo g_{e} (y)

Simplify

lo g_{e} (x) : ln (x)

= ln (4) + 2 ln (x) + 5 lo g_{e} (y)

Simplify

lo g_{e} (y) : ln (y)

= ln (4) + 2 ln (x) + 5 ln (y)

ln (4) = 2 ln (2)

= 2 ln (2) + 2 ln (x) + 5 ln (y)

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Frequently Asked Questions (FAQ)

What is log_{e}(4x^2y^5) ?
The solution to log_{e}(4x^2y^5) is 2ln(2)+2ln(x)+5ln(y)